... Jens, Artin's theorem or rule states that a subalgebra of an alternative algebra containing two members is associative. This can be used as a test to...
624
Jens Koeplinger
jens_koeplinger
Mar 19, 2009 8:02 pm
Hello Rick - ... algebra containing two members is associative. This can be used as a test to verify if a modification to a rule of multiplication for ...
626
jens@...
jens_koeplinger
Mar 20, 2009 5:54 pm
Rick - just quickly: Reading Conway, Smith, "On Quaternions and Octonions", chapters 6-8 (and in particular, chapters 8.1 through 8.3), I now speculate that...
627
ricklockyer
Mar 22, 2009 7:41 pm
... The algebraic structure (the 16 multiplication tables) are precursors to any applied multiplication of two octonions. The algebraic structure provides an...
628
jens@...
jens_koeplinger
Mar 23, 2009 6:00 pm
Rick - thanks for writing. ... You're speaking to the perfect forum, Rick! In this group (and its precursor), we've wrestled for years with algebras that would...
629
ricklockyer
Mar 24, 2009 4:01 am
Jens, ... Rigid body rotations have never factored into any of my work. The deal was this: I take axiomatically that octonion unlike non-scalar basis element...
630
jens@...
jens_koeplinger
Mar 24, 2009 1:09 pm
... No problem with me, we can leave the interest one-sided; I'm benefitting from our discussion a lot, so thanks for writing. I'll need a little time now to...
631
ricklockyer
Mar 25, 2009 3:08 pm
... Let me correct an off-the-cuff comment. i4 |-> -i4 leads to i0 * i4 = i4 |-> i0 * (-i4) = (-i4) == i0 * i4 = i4, and i4 * i4 = -1 |-> (-i4) * (-i4) = -1 ==...
632
detonacciones
Apr 7, 2009 12:43 pm
Dear Hypercomplex Numbers Group Members, Background. The following axioms were extracted from a number of texts posted at the following website -- ...
633
jens@...
jens_koeplinger
Apr 13, 2009 1:30 pm
Rick, Miguel - sorry for my slow replies, I'll be tied up until around the end of April. Thanks, Jens...
634
detonacciones
Apr 14, 2009 10:48 am
Jens, Understood! Look forward to your replies then. Regards, Miguel...
635
detonacciones
Apr 26, 2009 7:21 am
Dear Hypercomplex Numbers Group, As promised in my earlier post here on "Axioms for Dialectical Logic", this post contains a worked example of a...
636
detonacciones
May 3, 2009 2:24 am
Dear Hypercomplex Numbers Group Members, Hegel's <<Logik>>, originally published in 1812, has, in its first two Chapters, the following large-scale structure,...
637
Jens Koeplinger
jens_koeplinger
May 6, 2009 2:46 am
Miguel - sorry you're not receiving feedback here; maybe it's a bit over our capacity ... don't get me wrong, it is very interesting and important to...
638
ricklockyer
May 8, 2009 5:51 am
... part of your works even more. That bothers me, but I've got something coming (below) that needs lots of preparation. For now, I am happy to understand and...
639
detonacciones
May 11, 2009 1:37 am
Jens, Understood! What you're doing is important, and avails itself of an important -- and not very common -- opportunity. Best, in my view, to just give time...
640
detonacciones
May 16, 2009 4:15 am
Dear Hypercomplex Numbers Group Members, Part I. A New Model of the Universe. Pre-Note: The model of our <<kosmos>> presented herein is an 'ideo-graph-ical' ...
641
detonacciones
May 17, 2009 4:47 am
Dear Hypercomplex Number Group Members, Part II. A New, Non-Reductionist Model of the Universe, formulated by means of Non-Standard -- 'Meta-Natural" --...
642
Jens Koeplinger
jens_koeplinger
May 17, 2009 1:47 pm
Miguel - quick question: How many parts are you planning? I'm afraid that the material may not be compact enough for you to get a response here. I see your...
643
Jens Koeplinger
jens_koeplinger
May 17, 2009 2:15 pm
Hi Rick - just quickly: I'm currently writing on a paper that first brings some findings from different people, on octonions, into a harmonized notation, so...
644
detonacciones
May 19, 2009 4:16 am
Jens, There are three more, lengthy parts to the "New Model of the Universe" write-up, so I will stop posting it here now. Would like to post just two other...
645
detonacciones
May 19, 2009 4:20 am
Dear Hypercomplex Numbers Group Members, Principles Post 1 of 2 -- One CRUCIAL Point -- the symbolic logic used herein, and in some previous posts here, is NOT...
646
Rick Lockyer
ricklockyer
May 23, 2009 3:08 pm
Jens, Out on holiday now, very limited internet access. I will look at your draft when available. Rick...
647
Jens Koeplinger
jens_koeplinger
May 23, 2009 10:42 pm
... Enjoy! For now, I'm only referencing left-/right-octonions. Check out section 6.1, for solving differential equations. That'll be future work, maybe. All -...
648
ricklockyer
Jun 6, 2009 1:13 am
... section 6.1, for solving differential equations. That'll be future work, maybe. ... Jens, Got a chance to look over your paper and have a few comments....
649
jens@...
jens_koeplinger
Jun 8, 2009 1:23 pm
Hi Rick - sorry for the belated response. Thanks for reading over the paper! ... It's not me; the referenced publications use the different multiplication...
650
ricklockyer
Jun 8, 2009 4:24 pm
... Yes, it seemed less than the best way to describe it when I wrote it, but we did communicate successfully. These 4 are important groupings, so some cleave...
651
jens@...
jens_koeplinger
Jun 10, 2009 7:25 pm
Hi Rick - one thing up front: There's no pressure to respond "quickly"; we're patient, and you've been working on this for years so a few weeks won't make a...
652
ricklockyer
Jun 11, 2009 2:27 pm
... No it does not. The arrow directions are an essential part of the Fano plane representation of the octonion rules. For an example of unchanged, review the...
653
ricklockyer
Jun 12, 2009 1:35 pm
Jens, Have you figured it out yet? If not here is the deal. Examine the error terms in the composition law when (761) was changed to (167). I wrote ... Look at...
